Given a semisimple monoid category $\zeta$ with finitely many simple objects and an algebra $(A,\mu)$, it is claimed that bimodules of $\zeta$ over $A$ with a balanced tensor product $\otimes_A$ is again a monoid category.
ie, for $M,N\in\ _A\zeta_A$, the object $M\otimes_AN\in\ _A\zeta_A$, my question is how left and right morphism of $M\otimes_AN$ is constructed from its definition, which is actually a coequalizer ?